Extract the defined name from a cell

So on my Excel spreadsheet I can select cell B2 of Sheet1 and using the name box give that cell a name such as "Important_Cell".

I know using VBA I can access the cell using the name, such as:

Sheets(1).Range("Important_Cell").value = "This is it!"

But can I get that name FROM the cell?

I have tried the following:

name_string = Sheets(1).Range("B2").Name

But all that gave me in name_string was:

"='Sheet1'!$B$1"

Is there anyway to extract the actual defined name?

Thanks